Araştırma Makalesi
BibTex RIS Kaynak Göster

Numerical Oscillation Analysis for Gompertz Equation with One Delay

Yıl 2020, Cilt: 3 Sayı: 1, 1 - 7, 10.06.2020
https://doi.org/10.33401/fujma.623500

Öz

This paper concerns with the oscillation of numerical solutions of a kind of nonlinear delay differential equation proposed by Benjamin Gompertz, this equation usually be used to describe the population dynamics and tumour growth. We obtained some conditions under which the numerical solutions are oscillatory. The non-oscillatory behaviors of numerical solutions are also analyzed. Numerical examples are given to test our theoretical results.

Destekleyen Kurum

Natural Science Foundation of Guangdong Province

Proje Numarası

2017A030313031

Kaynakça

  • [1] J. Dzurina, I. Jadlovska, Oscillation theorems for fourth-order delay differential equations with a negative middle term, Math. Meth. Appl. Sci., 40 (2017), 7830-7842.
  • [2] K. M. Chudinov, On exact sufficient oscillation conditions for solutions of linear differential and difference equations of the first order with after effects, Russian Math., 62 (2018), 79-84.
  • [3] J. F. Gao, M. F. Song, M. Z. Liu, Oscillation analysis of numerical solutions for nonlinear delay differential equations of population dynamics, Math. Model. Anal., 16 (2011), 365-375.
  • [4] J. F. Gao, M. F. Song, Oscillation analysis of numerical solutions for nonlinear delay differential equations of hematopoiesis with unimodal production rate, Appl. Math. Comput., 264 (2015), 72-84.
  • [5] Q. Wang, Oscillation analysis of q-methods for the Nicholson’s blowflies model, Math. Meth. Appl. Sci., 39 (2016), 941-948.
  • [6] Y. Z. Wang, J. F. Gao, Oscillation analysis of numerical solutions for delay differential equations with real coefficients, J. Comput. Appl. Math., 337 (2018), 73-86.
  • [7] M. Bodnar, U. Foryss, Three types of simple DDE’s describing tumor growth, J. Biol. Syst., 15 (2007), 453-471.
  • [8] L. E. B. Cabrales, A. R. Aguilera, R. P. Jiméenéz, et al., Mathematical modeling of tumor growth in mice following low-level direct electric current, Math. Comput. Simulat., 78 (2008), 112-120.
  • [9] B. Gompertz, On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies, Philos. T. R. Soc. B, 115 (1825), 513-583.
  • [10] C. P. Winsor, The Gompertz Curve as a Growth Curve, Proc. Natl Acad. Sci., 18 (1932), 1-8.
  • [11] L. Ferrante, S. Bompadre, L. P. Leone, Parameter estimation in a Gompertzian stochastic model for tumor growth, Biometrics, 56 (2000), 1076-1081.
  • [12] M. J. Piotrowska, U. Forys, The nature of Hopf bifurcation for the Gompertz model with delays, Math. Comput. Model., 54 (2011), 2183-2198.
  • [13] M. J. Piotrowska, U. Forys, Analysis of the Hopf bifurcation for the family of angiogenesis models. J. Math. Anal. Appl., 382 (2011), 180-203.
  • [14] M. Bodnar, M. J. Piotrowska, U. Forys, Gompertz model with delays and treatment: Mathematical analysis, Math. Biosci. Eng., 10 (2013), 551-563.
  • [15] I. Gyori, G. Ladas, Oscillation Theory of Delay Differential Equations: with Applications, Oxford University Press, 1991.
  • [16] M. H. Song, Z. W. Yang, M. Z. Liu, Stability of q-methods for advanced differential equations with piecewise continuous arguments, Comput. Math. Appl., 49 (2005), 1295-1301.
Yıl 2020, Cilt: 3 Sayı: 1, 1 - 7, 10.06.2020
https://doi.org/10.33401/fujma.623500

Öz

Proje Numarası

2017A030313031

Kaynakça

  • [1] J. Dzurina, I. Jadlovska, Oscillation theorems for fourth-order delay differential equations with a negative middle term, Math. Meth. Appl. Sci., 40 (2017), 7830-7842.
  • [2] K. M. Chudinov, On exact sufficient oscillation conditions for solutions of linear differential and difference equations of the first order with after effects, Russian Math., 62 (2018), 79-84.
  • [3] J. F. Gao, M. F. Song, M. Z. Liu, Oscillation analysis of numerical solutions for nonlinear delay differential equations of population dynamics, Math. Model. Anal., 16 (2011), 365-375.
  • [4] J. F. Gao, M. F. Song, Oscillation analysis of numerical solutions for nonlinear delay differential equations of hematopoiesis with unimodal production rate, Appl. Math. Comput., 264 (2015), 72-84.
  • [5] Q. Wang, Oscillation analysis of q-methods for the Nicholson’s blowflies model, Math. Meth. Appl. Sci., 39 (2016), 941-948.
  • [6] Y. Z. Wang, J. F. Gao, Oscillation analysis of numerical solutions for delay differential equations with real coefficients, J. Comput. Appl. Math., 337 (2018), 73-86.
  • [7] M. Bodnar, U. Foryss, Three types of simple DDE’s describing tumor growth, J. Biol. Syst., 15 (2007), 453-471.
  • [8] L. E. B. Cabrales, A. R. Aguilera, R. P. Jiméenéz, et al., Mathematical modeling of tumor growth in mice following low-level direct electric current, Math. Comput. Simulat., 78 (2008), 112-120.
  • [9] B. Gompertz, On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies, Philos. T. R. Soc. B, 115 (1825), 513-583.
  • [10] C. P. Winsor, The Gompertz Curve as a Growth Curve, Proc. Natl Acad. Sci., 18 (1932), 1-8.
  • [11] L. Ferrante, S. Bompadre, L. P. Leone, Parameter estimation in a Gompertzian stochastic model for tumor growth, Biometrics, 56 (2000), 1076-1081.
  • [12] M. J. Piotrowska, U. Forys, The nature of Hopf bifurcation for the Gompertz model with delays, Math. Comput. Model., 54 (2011), 2183-2198.
  • [13] M. J. Piotrowska, U. Forys, Analysis of the Hopf bifurcation for the family of angiogenesis models. J. Math. Anal. Appl., 382 (2011), 180-203.
  • [14] M. Bodnar, M. J. Piotrowska, U. Forys, Gompertz model with delays and treatment: Mathematical analysis, Math. Biosci. Eng., 10 (2013), 551-563.
  • [15] I. Gyori, G. Ladas, Oscillation Theory of Delay Differential Equations: with Applications, Oxford University Press, 1991.
  • [16] M. H. Song, Z. W. Yang, M. Z. Liu, Stability of q-methods for advanced differential equations with piecewise continuous arguments, Comput. Math. Appl., 49 (2005), 1295-1301.
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Qian Yang 0000-0002-9316-7285

Qi Wang Bu kişi benim 0000-0003-3578-2551

Proje Numarası 2017A030313031
Yayımlanma Tarihi 10 Haziran 2020
Gönderilme Tarihi 23 Ocak 2019
Kabul Tarihi 20 Ocak 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 3 Sayı: 1

Kaynak Göster

APA Yang, Q., & Wang, Q. (2020). Numerical Oscillation Analysis for Gompertz Equation with One Delay. Fundamental Journal of Mathematics and Applications, 3(1), 1-7. https://doi.org/10.33401/fujma.623500
AMA Yang Q, Wang Q. Numerical Oscillation Analysis for Gompertz Equation with One Delay. Fundam. J. Math. Appl. Haziran 2020;3(1):1-7. doi:10.33401/fujma.623500
Chicago Yang, Qian, ve Qi Wang. “Numerical Oscillation Analysis for Gompertz Equation With One Delay”. Fundamental Journal of Mathematics and Applications 3, sy. 1 (Haziran 2020): 1-7. https://doi.org/10.33401/fujma.623500.
EndNote Yang Q, Wang Q (01 Haziran 2020) Numerical Oscillation Analysis for Gompertz Equation with One Delay. Fundamental Journal of Mathematics and Applications 3 1 1–7.
IEEE Q. Yang ve Q. Wang, “Numerical Oscillation Analysis for Gompertz Equation with One Delay”, Fundam. J. Math. Appl., c. 3, sy. 1, ss. 1–7, 2020, doi: 10.33401/fujma.623500.
ISNAD Yang, Qian - Wang, Qi. “Numerical Oscillation Analysis for Gompertz Equation With One Delay”. Fundamental Journal of Mathematics and Applications 3/1 (Haziran 2020), 1-7. https://doi.org/10.33401/fujma.623500.
JAMA Yang Q, Wang Q. Numerical Oscillation Analysis for Gompertz Equation with One Delay. Fundam. J. Math. Appl. 2020;3:1–7.
MLA Yang, Qian ve Qi Wang. “Numerical Oscillation Analysis for Gompertz Equation With One Delay”. Fundamental Journal of Mathematics and Applications, c. 3, sy. 1, 2020, ss. 1-7, doi:10.33401/fujma.623500.
Vancouver Yang Q, Wang Q. Numerical Oscillation Analysis for Gompertz Equation with One Delay. Fundam. J. Math. Appl. 2020;3(1):1-7.

Creative Commons License
The published articles in Fundamental Journal of Mathematics and Applications are licensed under a